RICHMOND — Gov. Robert F. McDonnell on Friday reappointed Helen E. Dragas to a second four-year term on the University of Virginia’s governing board, saying that the embattled board leader could help the school move past its recent leadership crisis.

Dragas drew fierce criticism this month for orchestrating the ouster of the school’s popular president, Teresa Sullivan. On Tuesday, Dragas reversed course and voted as part of a unanimous Board of Visitors to reinstate Sullivan. As the board chairman, Dragas holds the title of rector.

Her reappointment could raise questions about whether board rifts that opened up during the leadership crisis could reemerge in coming years, whether Sullivan would be able to work with Dragas after all that had transpired and how those dynamics would affect the university’s efforts to face long-term challenges.

McDonnell (R) and Sullivan brushed aside those questions.

“I am . . . concerned that the first female rector seemed to become the sole target of recent criticism,’’ the governor said in a statement. “While there is no doubt that the board made several mistakes in its actions, which it has publicly admitted, this is not a time for recrimination. It’s a time for reconciliation.”

Aside from Dragas, McDonnell largely remade the board Friday when he appointed five new members — nearly a third of the 17-member board that oversees the state’s flagship university.

“Governor McDonnell used great wisdom in appointing these members to the university’s board,” Sullivan said in a statement, “and I am grateful for his understanding of the challenges facing higher education. This is a group of distinguished individuals — from higher education and technology to government and health care — who will be able to hit the ground running.”

Sullivan’s statement did not mention Dragas, but the president sent the rector a bouquet and congratulatory note Friday morning.

Dragas, a Virginia Beach developer, was appointed to the board in 2008 by McDonnell’s Democratic predecessor, Timothy M. Kaine. Many Sullivan supporters had been demanding that Dragas step down or McDonnell not reappoint her.

McDonnell’s appointments take effect Sunday, but the General Assembly is required to hold a confirmation vote in January. Some lawmakers question whether Dragas could secure enough votes.

Dragas was named rector in 2011, a position the board bestowed on her. She will hold the title for another year.

‘I’m absolutely shocked’

Friday’s announcement drew swift condemnation from some quarters.

“I can’t understand why anybody would think this is a good idea’’ economics professor James Harrigan said. “I can’t understand why Helen Dragas would think this is a good idea.”

“I’m absolutely shocked,” said Joel Voss, 31, a graduate student in politics who helped coordinate the campaign for Sullivan’s reinstatement. “It’s clear that the University of Virginia community does not have confidence in her. . . . I don’t think we can forgive and forget.”

But some of the anger toward Dragas and her allies on the board subsided this week after the board rescinded the forced resignation of Sullivan.

“The most important thing was to get Terry back,” said John Simon, the university provost, who is Sullivan’s top academic deputy.

In a statement issued Friday, Dragas thanked McDonnell.

“Each of us on the board looks forward to working in a constructive and inclusive way with President Sullivan, along with students, faculty, alumni, and staff on tackling the broad challenges that face the university,’’ she wrote. “Together, I’m confident that we can preserve and enhance U-Va.’s greatness for present and future generations.”

The board has drawn intense scrutiny in recent weeks after the surprise removal of Sullivan — and the even more surprising reinstatement after protests on the historic campus in Charlottesville.

Governors generally appoint supporters and donors to fill about 200 seats on the governing boards that oversee the state’s universities — among the most coveted seats they can offer.

Turnover on the board

Friday’s names included friends but also educators, marking a change for the board.

McDonnell appointed Frank B. Atkinson, a longtime lobbyist and Republican activist, and Bobbie Kilberg, chief executive of the Northern Virginia Technology Council, who serves as a top donation bundler for GOP presidential candidate Mitt Romney. Both are McDonnell advisers who have donated tens of thousands of dollars to the governor, according to the Virginia Public Access Project, a nonpartisan tracker of money in politics.

He also appointed Linwood Rose, outgoing president of James Madison University; Edward Miller, an ex-officio U-Va. board member and former chief executive of Johns Hopkins Medicine; and Victoria Harker, chief financial officer for Gannett and chairman of the U-Va. Alumni Association.

Members, who may serve no more than two four-year terms, are not paid.

State university boards wield enormous power in hiring and firing the president, setting tuition rates, managing finances and approving faculty tenure.

Two members — medical executive W. Heywood Fralin, who helped organize Sullivan’s reinstatement, and lawyer Glynn D. Key — were not eligible for reappointment. Investor Robert D. Hardie was not reappointed to a second term.

McDonnell also filled the remainder of Mark J. Kington’s term after the vice rector resigned from the board last week, and a new board seat was created by the General Assembly.

McDonnell has said he looks for board members who share his goals of reducing college costs, increasing slots for in-state students and making schools more efficient. He has not generally reappointed board members selected by Kaine, but Dragas is an exception.

He had threatened to fire the entire board last week if it did not resolve the turmoil at the school, using a rarely used state law. Days later, the board reinstated Sullivan.

The board will meet to pick a new vice rector at its next meeting, likely at a retreat scheduled for mid-July.

McDonnell also asked Leonard Sandridge, a former U-Va. vice president, and Bill Goodwin, a former board member, to serve as senior advisers to the board.

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